Question

21. In the winter, the market demand for ice cream is Q = 30 – 3P, while the market supply is Q = P + 10. In the summertime, the quantity demanded is tripled at every price. What are the equilibrium prices and quantities in winter and summer? (a) Winter: P= 5, Q = 15 / Summer: P = 20,Q = 30 (b) Winter: P = 5, Q = 15 / Summer: P = 6, Q = 16 ((c) Winter: P= 5, Q = 15 / Summer: P= 8, Q = 18 (d) Winter: P = 5,Q = 30 / Summer: P= 10, Q = 40 (e) Winter: P= 5, Q = 30 / Summer: P= 6, Q = 40

Answer 1

Answer : The answer is option c.

In winter :

At equilibrium Demand = Supply occur. So,

30 - 3P = P + 10

=> 30 - 10 = P + 3P

=> 20 = 4P

=> P = 20 / 4

=> P = 5

Now from demand function we get,

Q = 30 - (3 * 5)

=> Q = 15

In summer :

The demand function become :

Q = 3 * (30 - 3P) [As quantity demanded is tripled at every price level]

=> Q = 90 - 9P

At equilibrium Demand = Supply occur. So,

90 - 9P = P + 10

=> 90 - 10 = P + 9P

=> 80 = 10P

=> P = 80 / 10

=> P = 8

From demand function we get,

Q = 90 - (9 * 8)

=> Q = 18

Therefore, option c is correct.